Introduction to Pricing Approach

Bond options give the holder the right but not the obligation to either buy or sell the underlying bond on a set of established dates for a pre-specified fixed price. Just as for equivalent options written on stocks, commodities or currencies, the decision to exercise the option at any given date is dependent on the observed relativity between the market value of the underlying asset and the strike price stipulated by the option. However, for bond options, the process of 'forecasting' the possible distribution of underlying bond prices is more complex than it is for other underlying assets. The reason for that is because the bond values themselves are contingent on the level of the yield curve at all future dates, and it is the process of establishing the future distribution of these yield curves that gives rise to most of the complexity associated with valuing these options.

The valuation routines used to value American and Bermudan bond options are closely related to those used for callable and puttable bonds. That is, the option itself can be valued using 2 alternative implementations of the procedure used for valuing bonds with embedded options. First, value the bond assuming the existence of an embedded option with the same characteristics as the option under consideration. Then value the vanilla bond and compute option value as the difference between the two bond values.

The model actually uses an equivalent but more efficient procedure that is closely analogous to the standard backward induction methods used for Bermudan and American style options written on underlying assets such as shares of stock. This more direct approach is quicker because it only requires one pass through the constructed interest rate lattice, instead of the two separate passes that are required if the "with and without" method is used.